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Tables for epidemiologists

  • 2 × 2 and 2 × 2 stratified table for longitudinal, cohort study, case–control, and matched case–control data
  • Odds ratio, incidence ratio, risk ratio, risk difference, and attributable fraction
  • Confidence intervals for the above
  • Chi-squared, Fishers’s exact, and Mantel–Haenszel tests
  • Tests for homogeneity
  • Choice of weights for stratified tables: Mantel–Haenszel, standardized, or user specified
  • Exact McNemar test for matched case–control data
  • Tabulated odds and odds ratios
  • Score test for linear trend

Stata has a set of commands for dealing with 2 x 2 tables, including stratified tables, known collectively as the epitab commands. To calculate appropriate statistics and suppress inappropriate statistics, these commands are organized in the same way that epidemiologists conceptualize data.

Stata’s ir command is used with incidence-rate (incidence density or person-time) data; point estimates and confidence intervals for the incidence-rate ratio and difference are calculated, along with the attributable or prevented fractions for the exposed and total populations.

Stata’s cs command is used with cohort study data with equal follow-up time per subject. Risk is then the proportion of subjects who become cases. Point estimates and confidence intervals for the risk difference, risk ratio, and (optionally) the odds ratio are calculated, along with attributable or prevented fractions for the exposed and total population.

Stata’s cc command is used with case–control and cross-sectional data. Point estimates and confidence intervals for the odds ratio are calculated along with attributable or prevented fractions for the exposed and total population.

mcc is used with matched case–control data. It calculates McNemar’s chi-squared, point estimates, and confidence intervals for the difference, ratio, and relative difference of the proportion with the factor, along with the odds ratio.

All these commands come in two flavors: their normal forms and an “immediate” form. In their normal forms, the commands form counts by summing the dataset in use. In their immediate forms, the data are specified on the command line.

For instance, Boice and Monson (1977 and reprinted in Rothman, Greenland, and Lash 2008, 244) reported on breast cancer cases and person-years of observations for women with tuberculosis who were repeatedly exposed to multiple X-ray fluoroscopies and for those not exposed:

X-ray fluoroscopy Exposed Unexposed
Breast cancer cases 41 15 Person years 28,010 19,017

Using the immediate form of ir, you specify the values in the table following the command:

. iri 41 15 28010 19017
Exposed Unexposed Total
Cases 41 15 56
Person-time 28010 19017 47027
Incidence rate .0014638 .0007888 .0011908
Point estimate [95% Conf. Interval]
Inc. rate diff. .000675 .0000749 .0012751
Inc. rate ratio 1.855759 1.005684 3.6093 (exact)
Attr. frac. ex. .4611368 .0056519 .722938 (exact)
Attr. frac. pop .337618
(midp) Pr(k>=41) = 0.0177 (exact)
(midp) 2*Pr(k>=41) = 0.0355 (exact)

The grander ir command itself can work with individual-level or aggregate data and also work with stratified data. Rothman, Greenland, and Lash (2008, 264) report results from Doll and Hill (1966) on age-specific coronary disease deaths among British male doctors in relation to cigarette smoking:

Smokers Nonsmokers Age Deaths Person-years Deaths Person-years
35-44 32 52,407 2 18,790 45-54 104 43,248 12 10,673 55-64 206 28,612 28 5,710 65-74 186 12,663 28 2,585 75-84 102 5,317 31 1,462

We have entered these data into Stata:

. list, separator(0)
age smokes deaths pyears
1. 35-44 1 32 52,407
2. 35-44 0 2 18,790
3. 45-54 1 104 43,248
4. 45-54 0 12 10,673
5. 55-64 1 206 28,612
6. 55-64 0 28 5,710
7. 65-74 1 186 12,663
8. 65-74 0 28 2,585
9. 75-84 1 102 5,317
10. 75-84 0 31 1,462

We can obtain the Mantel–Haenszel combined estimate of the incidence-rate ratio, along with 90% confidence intervals, by typing

. ir deaths smokes pyears, by(age) level(90) Test of homogeneity (M-H) chi2(4) = 10.41 Pr>chi2 = 0.0340
age IRR [90% Conf. Interval] M-H Weight
35-44 5.736638 1.704271 33.61646 1.472169 (exact)
45-54 2.138812 1.274552 3.813282 9.624747 (exact)
55-64 1.46824 1.044915 2.110422 23.34176 (exact)
65-74 1.35606 .9626026 1.953505 23.25315 (exact)
75-84 .9047304 .6375194 1.305412 24.31435 (exact)
Crude 1.719823 1.437544 2.0688 (exact)
M-H combined 1.424682 1.194375 1.699399

Rothman and Greenland (1998, 264) obtain the standardized incidence-rate ratio and 90% confidence intervals, weighting each age category by the population of the exposed group, thus producing the standardized mortality ratio (SMR). This calculation can be reproduced by specifying by(age) to indicate that the table is stratified, and istandard to specify that we want the internally standardized rate:

. ir deaths smokes pyears, by(age) level(90) istandard
age IRR [90% Conf. Interval] Weight
35-44 5.736638 1.704271 33.61646 52407 (exact)
45-54 2.138812 1.274552 3.813282 43248 (exact)
55-64 1.46824 1.044915 2.110422 28612 (exact)
65-74 1.35606 .9626026 1.953505 12663 (exact)
75-84 .9047304 .6375194 1.305412 5317 (exact)
Crude 1.719823 1.437544 2.0688 (exact)
I. Standardized 1.417609 1.186541 1.693676

If we want the externally standardized ratio (weights proportional to the population of the unexposed group), we can substitute estandard for istandard in the command above.

References

Boice, J. D., and R. R. Monson. 1977.
Breast cancer in women after repeated fluoroscopic examinations of the chest. Journal of the National Cancer Institute 59: 823–832.
Doll, R., and A. B. Hill. 1966.
Mortality of British doctors in relation to smoking: observations on coronary thrombosis. In Epidemiological Approaches to the Study of Cancer and Other Chronic Diseases, ed. W. Haenszel. National Cancer Institute Monograph 19: 205–268.
Rothman, K. J., S. Greenland, and T. L. Lash. 2008.
Modern Epidemiology. 3rd ed (Revised). Philadelphia: Lippincott Williams & Wilkins.
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